! Importance of Particle Adhesion ! Importance of Particle Adhesion - - PowerPoint PPT Presentation

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• G. Ahmadi

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! ! Importance of Particle Adhesion Importance of Particle Adhesion ! ! History of Particle Adhesion History of Particle Adhesion ! ! Method of measurement of Adhesion Method of measurement of Adhesion ! ! Adhesion Induced Deformation Adhesion Induced Deformation ! ! JKR and non JKR and non-

• JKR Theory

JKR Theory ! ! Role of Electrostatic Forces Role of Electrostatic Forces ! ! Conclusions Conclusions

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Books:

• D. S. Rimai and D. J. Quesnel, Fundamentals of Particle Adhesion, Global Press (available

through the Adhesion Society at adhesion society.org) (2001).

• D. J. Quesnel, D. S. Rimai, and L. H. Sharpe, Particle Adhesion: Applications and Advances,

Taylor and Francis (2001)

• D. S. Rimai and L. H. Sharpe, Advances in Particle Adhesion, Gordon and Breach

Publishers (1996).

• D. S. Rimai, L. P. DeMejo, and K. L. Mittal, Fundamentals of Adhesion and Interfaces, VSP

Press (1995).

• K. L. Mittal, Particles on Surfaces: Detection, Adhesion, and Removal, 1, 2 and 3, Plenum

Press (1986), (1988), (1990), (1995).

• A. Zimon, Adhesion of Dust and Powders, Consultants Bureau (1976).
• T. B. Jones, Electromechanics of Particles, Cambridge University Press (1995).
• J. Israelachvili, Intermolecular and Surface Forces, Academic Press (1992).
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Articles

• H. Krupp, Advan. Colloid Interface Sci. 1, 111 (1967).
• K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London, Ser A 324, 301 (1971).
• D. S. Rimai and L. P. DeMejo, Annu. Rev. Mater. Sci.26, 21 (1996).
• D. S. Rimai and A. A. Busnaina, Particulate Science and Technology 13, 249 (1995).
• B. Gady, D. Schleef, R. Reifenberger, D. S. Rimai, and L. P. DeMejo, Phys. Rev. B 53, 8065 (1996).
• N. S. Goel and P. R. Spencer, Polym. Sci. Technol. 9B, 763 (1975).
• D. Maugis and H. M. Pollock, Acta Metall. 32, 1323 (1984).
• L. N. Rogers and J. Reed, J. Phys. D 17, 677 (1984).
• K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London Ser. A 324, 301 (1971).
• B. V. Derjaguin, V. M. Muller, and Yu. P. Toporov, J. Colloid Interface Sci. 53, 314 (1975).
• D. Tabor, J. Colloid Interface Sci. 58, 2 (1977).
• V. M. Muller, V. S. Yushchenko, and B. V. Derjaguin, J. Colloid Interface Sci. 77, 91 (1980).
• D. J. Quesnel, D. S. Rimai, and L. P. DeMejo, J. Adhesion 51, 49 (1995).

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Articles Soltani, M. and Ahmadi, G., On Particle Adhesion and Removal Mechanisms in Turbulent Flows, J. Adhesion Science Technology, J. Adhesion Science Technology Vol. 7, 763-785 (1994). Soltani, M. and Ahmadi, G., On Particle Removal Mechanisms Under Base Acceleration, J. Adhesion Vol. 44, 161-175 (1994). Soltani, M., Ahmadi, G., Bayer, R.G. and Gaynes, M.A., Particle Detachment Mechanisms from Rough Surfaces Under Base Acceleration, J. Adhesion Science Technology Vol. 9, 453-473 (1995). Soltani, M. and Ahmadi, G., Direct Numerical Simulation of Particle Entrainment in Turbulent Channel Flow, Physics Fluid A Vol. 7 647-657(1995). Soltani, M. and Ahmadi, G., Particle Detachment from Rough Surfaces in Turbulent Flows,

• J. Adhesion Vol. 51, 87-103 (1995).

Soltani, M. and Ahmadi, G., Detachment of Rough Particles with Electrostatic Attraction From Surfaces in Turbulent Flows, J. Adhesion Sci. Technol., Vol. 13, pp. 325-355 (1999). Soltani, M., Ahmadi, G. and Hart, S. C., Electrostatic Effects on Resuspension of Rigid-Link Fibers in Turbulent Flows, Colloids Surfaces, Vol. 165, pp. 189-208 (2000).

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Technologically important Technologically important

• A. Semiconductor fabrication
• A. Semiconductor fabrication
• B. Electrophotography
• B. Electrophotography
• C. Pharmaceuticals
• C. Pharmaceuticals
• D. Paint
• D. Paint
• E. Agriculture
• E. Agriculture
• F. Aeronautics and space
• F. Aeronautics and space
• G. Etc.
• G. Etc.
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Fundamentally Important Fundamentally Important

• A. Avoids confounding interactions
• A. Avoids confounding interactions

(gravity, applied loads, etc.) (gravity, applied loads, etc.)

• B. Allows thermodynamic parameters such
• B. Allows thermodynamic parameters such

as work of adhesion to be determined. as work of adhesion to be determined.

• C. Allows present understanding of
• C. Allows present understanding of

adhesion to be tested. adhesion to be tested.

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• Particles are attracted to substrates (or

Particles are attracted to substrates (or

• ther
• ther particles) via certain types of

particles) via certain types of

• interactions. These
• interactions. These interactions create

interactions create stresses between the stresses between the materials. These

• materials. These

stresses, in turn, create strains stresses, in turn, create strains that may that may be be large or small, elastic or plastic. large or small, elastic or plastic.

• Only by understanding both the

Only by understanding both the interactions interactions and the and the mechanical mechanical response of the response of the materials to these materials to these interactions can adhesion interactions can adhesion be understood. be understood.

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• This presentation will focus on particle

This presentation will focus on particle

• adhesion. However, just as the JKR
• adhesion. However, just as the JKR

theory describes adhesion between theory describes adhesion between macroscopic bodies, the concepts macroscopic bodies, the concepts presented presented can be readily generalized to other can be readily generalized to other situations. situations.

• The JKR model is the underlying theory on

The JKR model is the underlying theory on which most of our present understanding of which most of our present understanding of adhesion is based. adhesion is based.

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• Hertz (circa 1890): Proposed that a rigid indenter,

Hertz (circa 1890): Proposed that a rigid indenter, acting under a compressive load P, would cause a acting under a compressive load P, would cause a deformation of radius deformation of radius a a in a substrate having a in a substrate having a Young Young’ ’s modulus s modulus E E and a Poisson ratio and a Poisson ratio ν ν given by given by

• 1930s:

1930s: Derjaguin Derjaguin and Bradley independently and Bradley independently proposed proposed the concept of adhesion the concept of adhesion-

• induced

induced deformations between deformations between particles and substrates. particles and substrates. Derjaguin Derjaguin assumed that the assumed that the adhesion adhesion-

• induced contact radius can be calculated

induced contact radius can be calculated from from Hertzian Hertzian theory. theory.

( )

E 4 RP 1 3 a

2 3

ν − =

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• 1937: Hamaker proposes that surface forces

1937: Hamaker proposes that surface forces were related to the density of atoms in the were related to the density of atoms in the particle and substrate, particle and substrate, n nP

P and

and n nS

S, respectively.

, respectively. Hamaker further proposed that the interaction Hamaker further proposed that the interaction parameter parameter A A (commonly referred to as the (commonly referred to as the Hamaker constant) was related to London Hamaker constant) was related to London dispersion forces by dispersion forces by The load The load P P is then given by is then given by

λ π

S P 2

n n A =

2

6 z R A P =

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• By combining this result with the

By combining this result with the Hertzian Hertzian indenter model, one sees that the indenter model, one sees that the Derjaguin Derjaguin model relates the contact radius to the model relates the contact radius to the particle radius by particle radius by

( )

2 2 2 3

8 1 R z A a ν − =

4

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• 1956:

1956: Lifshitz Lifshitz proposes a model relating the London proposes a model relating the London dispersion forces (i.e. the major component of van dispersion forces (i.e. the major component of van der der Waals interactions in most systems) to the generation Waals interactions in most systems) to the generation

• f electromagnetic waves caused by instantaneous
• f electromagnetic waves caused by instantaneous

dipole fluctuations. Surface forces are shown to have dipole fluctuations. Surface forces are shown to have an effective range, rather than being contact forces. an effective range, rather than being contact forces.

• 1967:

1967: Krupp Krupp proposes adhesion proposes adhesion-

• induced plastic

induced plastic

• deformations. He proposed that the adhesion
• deformations. He proposed that the adhesion-
• induced stresses between a particle and a substrate

induced stresses between a particle and a substrate could exceed the yield strength of at least one of the could exceed the yield strength of at least one of the contacting materials. contacting materials.

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• Circa 1969: David Tabor approaches Ken

Circa 1969: David Tabor approaches Ken Johnson about a rather perplexing student Johnson about a rather perplexing student Tabor has that does not seem to believe Hertz. Tabor has that does not seem to believe Hertz.

• 1971: The JKR (Johnson, Kendall, and Roberts)

1971: The JKR (Johnson, Kendall, and Roberts) theory of adhesion is published. This theory theory of adhesion is published. This theory recognized that both tensile and compressive recognized that both tensile and compressive interactions contribute to the total contact interactions contribute to the total contact

• radius. JKR model is derived using contact
• radius. JKR model is derived using contact
• mechanics. It assumes that there are no long
• mechanics. It assumes that there are no long-
• range interactions.

range interactions.

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• 1975:

1975: Derjaguin Derjaguin, Muller, and , Muller, and Toporov Toporov generalize the original generalize the original Derjaguin Derjaguin model of model of adhesion to include tensile interactions. This is adhesion to include tensile interactions. This is the DMT theory. the DMT theory.

• 1977:

Tabor highlights differences in 1977: Tabor highlights differences in assumptions and predictions between JKR and assumptions and predictions between JKR and DMT theories. Also shows that, as long as the DMT theories. Also shows that, as long as the meniscus height is large compared to the range meniscus height is large compared to the range

• f surface forces, the JKR assumption of no
• f surface forces, the JKR assumption of no

long long-

• range interactions is valid.

range interactions is valid.

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• 1980: Muller,

1980: Muller, Yushchenko Yushchenko, and , and Derjaguin Derjaguin (MYD) propose a general model that purports (MYD) propose a general model that purports that both the JKR and DMT theories are subsets that both the JKR and DMT theories are subsets

• f the MYD model. They further divide the
• f the MYD model. They further divide the

universe between small particle, high modulus, universe between small particle, high modulus, low surface energy systems (DMT) and larger low surface energy systems (DMT) and larger particle, lower modulus, higher surface energy particle, lower modulus, higher surface energy (JKR systems). (JKR systems).

• 1984:

1984: Maugis Maugis and Pollock generalize the JKR and Pollock generalize the JKR theory to include adhesion theory to include adhesion-

• induced plastic

induced plastic deformations. deformations.

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• 1. Centrifugation
• 1. Centrifugation
• A. Better on large (R>20
• A. Better on large (R>20 µ

µm) m)

• B. Slow
• B. Slow
• C. Well established technique
• C. Well established technique
• D. Minimal interactions
• D. Minimal interactions
• E. Good statistics
• E. Good statistics
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• 2. Electrostatic Detachment
• 2. Electrostatic Detachment
• A. Medium to large particles (R>5
• A. Medium to large particles (R>5 µ

µm) m)

• B. Interaction with electric field
• B. Interaction with electric field
• C. Good statistics
• C. Good statistics
• 3. Hydrodynamic Detachment
• 3. Hydrodynamic Detachment
• A. Small particles (R<0.5
• A. Small particles (R<0.5 µ

µm) m)

• B. Good statistics
• B. Good statistics
• C. Introduces a fluid
• C. Introduces a fluid
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• 4. Atomic Force Techniques
• 4. Atomic Force Techniques
• A. Measures attractive as well as
• A. Measures attractive as well as

removal force removal force

• B. Can exert precise loads on particles
• B. Can exert precise loads on particles
• C. Short and variable time scales
• C. Short and variable time scales
• D. Can distinguish force mechanisms
• D. Can distinguish force mechanisms
• E. Poor statistics
• E. Poor statistics
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• 5. Contact Area Technique
• 5. Contact Area Technique
• A. Good statistics
• A. Good statistics
• B. Forces not directly measured.
• B. Forces not directly measured.
• C. Equilibrium measurement
• C. Equilibrium measurement
• D. Need spherical particles
• D. Need spherical particles
• E. Wide range of particle sizes
• E. Wide range of particle sizes

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6.

• 6. Nanoindentor

Nanoindentor

• A. Easy to interpret measurements
• A. Easy to interpret measurements
• B. Readily repeatable
• B. Readily repeatable
• C. Simulation of particle adhesion
• C. Simulation of particle adhesion

rather than actual rather than actual measurement. measurement.

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7.

• 7. Israelachvili

Israelachvili Surface Force Apparatus Surface Force Apparatus

• A. Uses crossed cylinders rather
• A. Uses crossed cylinders rather

than particles than particles

• B. Cylinders can be coated with
• B. Cylinders can be coated with

materials of interest materials of interest

• C. Simulation of particle adhesion
• C. Simulation of particle adhesion
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There is a total energy There is a total energy U UT

T of a system, where

• f a system, where

where where U UE

E is the elastically stored energy

is the elastically stored energy U UM

M is the mechanical energy associated

is the mechanical energy associated with the applied load. with the applied load. U US

S is the total surface energy = w

is the total surface energy = wA

Aπ

πa a2

2

S M E T

U U U U + + =

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The JKR equation is given by: The JKR equation is given by:

( )

[ ]

{ }

2 / 1 2 A A A 3

R w 3 P R w 6 R w 3 P K R a π + π + π + =

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1.

• 1. The deformations are elastic.

The deformations are elastic. 2.

• 2. The contact radius is small

The contact radius is small compared to the particle radius. compared to the particle radius. 3.

• 3. All interactions are localized to

All interactions are localized to within the contact region, within the contact region, i.e. i.e. there are no long there are no long-

• range

range interactions. interactions.

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High elastic High elastic modulus spherical modulus spherical particles on particles on elastomeric elastomeric substrates. substrates.

Polystyrene on Polyurethane

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Polystyrene particles on a silicon wafer

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R0.5 (µm0.5)

1 2

Conntact Radius (microns)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

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Burnham, Colton, and Pollock (Phys. Burnham, Colton, and Pollock (Phys. Rev.

• Rev. Lett
• Lett. 69, 144 (1992)) measured

. 69, 144 (1992)) measured the attractive force between an AFM the attractive force between an AFM cantilever tip and a flat graphite cantilever tip and a flat graphite

• surface. They reported that the range
• surface. They reported that the range
• f attractive forces was too great to be
• f attractive forces was too great to be

explained in terms of van explained in terms of van der der Waals Waals forces. forces.

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Horn and Smith (Nature 366, 442 (1993); Horn and Smith (Nature 366, 442 (1993); Science 256, 362 (1992); J. Electrostatics Science 256, 362 (1992); J. Electrostatics 26, 291 (1991)) reported an increase in 26, 291 (1991)) reported an increase in detachment force between two flat silica detachment force between two flat silica substrates, one of which had been coated substrates, one of which had been coated with with dimethyethoxysilane

• dimethyethoxysilane. The increase in

. The increase in adhesion was associated with a transfer of adhesion was associated with a transfer of charge from one material to the other. charge from one material to the other.

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Dickinson (see, for example, Dickinson (see, for example, Fundamentals of Adhesion and Fundamentals of Adhesion and Interfaces Interfaces, Rimai, DeMejo, and Mittal , Rimai, DeMejo, and Mittal (eds.), pp. 179 (eds.), pp. 179-

• 204 (1995) reported the

204 (1995) reported the emission of charged particles generated emission of charged particles generated upon the fracture of a material upon the fracture of a material (fractoemissions). (fractoemissions).

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• Van

Van der der Waals forces are electrodynamic and are Waals forces are electrodynamic and are expected to be short range. Under certain expected to be short range. Under certain circumstances they may contribute significantly to circumstances they may contribute significantly to adhesion. adhesion.

• There are long

There are long-

• range interactions that contribute

range interactions that contribute to adhesion. These may be due to electrostatic to adhesion. These may be due to electrostatic interactions. interactions.

• There is evidence that adhesion has long

There is evidence that adhesion has long-

• range

range

• contributions. If this is correct, is the JKR theory,
• contributions. If this is correct, is the JKR theory,

which is based on contact mechanics, appropriate? which is based on contact mechanics, appropriate?

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Consider a spherical toner particle of Consider a spherical toner particle of radius radius R R = 6 = 6 µ µm and m and q/m q/m = 15 = 15 µ µC/g. C/g. ⇒ ⇒ q q = 1.4 x 10 = 1.4 x 10-

• 14

14 C.

C. ⇒ ⇒ σ σ = 3 x 10 = 3 x 10-

• 5

5 C/m

C/m2

2.

.

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Van Der Waals Electrostatic

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For a single, dielectric, spherical particle For a single, dielectric, spherical particle with a uniform charge distribution with a uniform charge distribution

2 2 2 Im

2 4 4 1 2 4 1 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = R R R q F σ π ε π ε π

( )

2 2 2 2 2 Im

4 4 1 ε σ π σ π ε π R R F = =

FIm = 12 nN FIm = 12 nN

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van van der der Waals Attraction: Waals Attraction: F FVW

VW = 625

= 625 nN nN

2 VW

z 6 R A F =

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Define Define R Rcrit

crit by

by F FVW

VW =

= F FIm

Im

If: If: A A = 10 = 10-

• 19

19 J

J z z0

0 = 4

= 4 Å Å ⇒ ⇒ R Rcrit

crit = 0.5 mm

= 0.5 mm For For R R < < R Rcrit

crit: van

: van der der Waals dominated Waals dominated For For R R > > R Rcrit

crit: electrostatic dominated

: electrostatic dominated However: Both forces contribute to However: Both forces contribute to adhesion. adhesion.

2 2

6 σ π ε z A Rcrit =

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Schematic illustration of experimental setup. The Schematic illustration of experimental setup. The larger toner particles fix the size of the air gap larger toner particles fix the size of the air gap while the applied electric field cause the smaller while the applied electric field cause the smaller particle to transfer from the photoconductor (top) particle to transfer from the photoconductor (top) to the receiver (bottom). to the receiver (bottom).

Spacer Particle

Particle

d D Chrome cermet receiver

Photoconductor

12

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2 4 6 8 10 12 14

Force (nN)

100 200 300 400

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• Thus far, it would appear that the

Thus far, it would appear that the JKR contact mechanics assumption JKR contact mechanics assumption is valid. is valid.

• However,

if electrostatic forces However, if electrostatic forces become more significant, long become more significant, long-

• range

range interactions would have to be taken interactions would have to be taken into account. into account.

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2 2

6 σ π ε z A Rcrit =

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Increase the size of the particle. Increase the size of the particle. Electrostatic Electrostatic forces as forces as R R2

2 whereas van

whereas van der der Waals forces Waals forces vary linearly with vary linearly with R R. . Increase the surface Increase the surface-

• charge density.

charge density. The The critical radius varies as 1/ critical radius varies as 1/σ σ2

2.

. Decrease the surface energy/Hamaker Decrease the surface energy/Hamaker constant.

• constant. Examples include coating a surface

Examples include coating a surface with Teflon or zinc stearate. with Teflon or zinc stearate.

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Add asperities to the particle. Add asperities to the particle. These serve as These serve as physical separations that reduce adhesion physical separations that reduce adhesion (Tabor and Fuller (Proc. R. Soc. (Tabor and Fuller (Proc. R. Soc. Lond

• Lond. A 345,

. A 345, 327 (1975); Schaefer et al. J. Adhesion 327 (1975); Schaefer et al. J. Adhesion Sci Sci. . Technol

• Technol. 9, 1049 (1995))

. 9, 1049 (1995)) Add neighboring particles having a similar Add neighboring particles having a similar charge. charge. ( (Goel Goel and Spencer, in and Spencer, in Adhesion Adhesion Science and Technology Part B Science and Technology Part B, L. H. Lee , L. H. Lee (ed.)). (ed.)).

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Localize charge to specific areas on Localize charge to specific areas on surface of the particle rather than surface of the particle rather than uniformly distributing it uniformly distributing it – – the so the so-

• called

called “ “charged patch model. charged patch model.” ” (D.A. (D.A. Hays, in Hays, in Fundamentals of Adhesion Fundamentals of Adhesion and Interfaces and Interfaces, D. S. Rimai, L. P. , D. S. Rimai, L. P. DeMejo, and K. L. Mittal (eds.)) DeMejo, and K. L. Mittal (eds.))

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F neigh =40 nN

Neighbor Forces Acting on Particle Neighbor Forces Acting on Particle

F elect = σ2 Ac / 2ε0

F = 40 nN

+ + +

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Assume that the particle charge is localized to a Assume that the particle charge is localized to a discreet section of the particle discreet section of the particle Electrostatic contribution to attractive force Electrostatic contribution to attractive force F FE

E

is given by is given by A AC

C is the contact area

is the contact area σ σ is the charge density is the charge density

C 2 E

2 A F ε σ =

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Note: Note: These particles are irregularly These particles are irregularly-

• shaped

shaped No silica No silica: : Particle radius = 4 Particle radius = 4µ µm m W WA

A = 0.05 J/m

= 0.05 J/m2

2, q/m

, q/m = 37 = 37 + + 3 3 µ µC/g, C/g, ρ ρ = 1.2 g/cm = 1.2 g/cm3

3

From JKR theory: From JKR theory: Measured value: Measured value: F FS

S = 970

= 970 nN nN

nN 943 R w 2 3 F

A S

= π =

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2% Silica 2% Silica: : Assume JKR contact radius = 196 nm Assume JKR contact radius = 196 nm r rsilica

silica = 30 nm,

= 30 nm, ρ ρsilica

silica = 1.75 g/cm

= 1.75 g/cm3

3.

. ⇒ ⇒have about 10 silica particles within the contact have about 10 silica particles within the contact zone. zone. Approximate JKR removal force by Approximate JKR removal force by Measured: F Measured: FS

S’

’ = 70 = 70 nN nN

nN 39 r w 2 3 n F

A S

= π = ′

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⇒ ⇒ F FIm

Im = 20

= 20 – – 40 40 nN nN

( )2

2 Im

2 4 R q F ε π α =

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Patch charge density limited by dielectric Patch charge density limited by dielectric strength of air. strength of air. ⇒ ⇒ F FE

E ≈

≈ 30 30 nN nN

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• If

the particle has sufficient If the particle has sufficient irregularity, irregularity, van van der der Waals forces, Waals forces, electrostatic electrostatic image forces, and image forces, and charged charged-

• patch forces

patch forces all predict all predict about the same size force, about the same size force, which which is comparable to experimentally is comparable to experimentally determined detachment force. determined detachment force.

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• For

small, spherical particles, adhesion For small, spherical particles, adhesion appears to be dominated by van appears to be dominated by van der der Waals Waals interactions. interactions.

• As the particles become bigger or more

As the particles become bigger or more irregular, electrostatics become more irregular, electrostatics become more important. important.

• van

van der der Waals interactions can be reduced, Waals interactions can be reduced, even for small, spherical particles, to the even for small, spherical particles, to the point point where electrostatic forces can become where electrostatic forces can become dominant. dominant.

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• The electric charge contribution increases

The electric charge contribution increases with increasing charge and the presence of with increasing charge and the presence of neighboring particles. neighboring particles.

• These results hold for macroscopic systems

These results hold for macroscopic systems as well as microscopic ones. as well as microscopic ones.

• Electrostatic interactions are long

Electrostatic interactions are long-

• range.

range.

• JKR theory should be extended to allow for

JKR theory should be extended to allow for long long-

• range interactions

range interactions

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